# PAMSAC

**PAMSAC** (**Proportional Approval Method using Squared loads, Approval removal and Coin-flip approval transformation**) is a system of proportional representation that uses approval voting, based on Ebert's Method. It was developed by Toby Pereira to restore monotonicity to Ebert's Method.

Ebert's method essentially looks for the result that gives voters the most equal representation, which can be at the expense of monotonicity. In the following example, there are two voters, and A, B, C and D are candidates. Two candidates are to be elected. The approval ballots are as follows:

1 voter: A, B, C

1 voter: A, B, D

The election of candidates A and B or the election of candidates C and D are considered equal under Ebert's Method, as under both results, all voters are equally represented. But since A and B have been unanimously approved, this is arguably the better result. The coin-flip approval transformation (CFAT) used in PAMSAC was designed to resolve this. For every candidate that a voter approves, the voter is effectively split into two, where one half of the split voter approves the candidate and one half does not. The transformed ballots would be as follows:

1/8 voters: A, B, C

1/8 voters: A, B

1/8 voters: A, C

1/8 voters: B, C

1/8 voters: A

1/8 voters: B

1/8 voters: C

1/8 voters: -

1/8 voters: A, B, D

1/8 voters: A, B

1/8 voters: A, D

1/8 voters: B, D

1/8 voters: A

1/8 voters: B

1/8 voters: D

1/8 voters: -

Taking away half the approvals in this way is more detrimental to the CD result than the AB result, since under the CD result, voters were each only represented by one candidate to start with, so under the transformed result, half the voters are effectively left unrepresented. Under the AB result, since voters were already each represented by two candidates, removing half of the approvals still leaves three quarters of the voters with some representation. Applying Ebert's Method to the transformed ballots results in the election of A and B.

Ebert's Method can still fail monotonicity with CFAT applied, so when a potential winning set of candidates is considered in PAMSAC, the measure of a set of candidates is the minimum achievable sum of squared voter loads after detrimental approvals have been removed. The approvals are removed before CFAT is applied. The removal of detrimental approvals is actually equivalent to allowing the load from a candidate to be unequally spread across their voters. As such PAMSAC is the same as var-Phragmén with CFAT.

## Further reading

The original PAMSAC paper can be found here.